Caruso, NoeMichelangeli, AlessandroNovati, Paolo2018-11-202018-11-202018-11https://openscience.sissa.it/handle/1963/35327We discuss, in the context of inverse linear problems in Hilbert space, the notion of the associated infinite-dimensional Krylov subspace and we produce necessary and sufficient conditions for the Krylov-solvability of the considered inverse problem. The presentation is based on theoretical results together with a series of model examples, and it is corroborated by specific numerical experiments.eninverse linear problems,in nite-dimensional Hilbert spaceill-posed problemsorthonormal basis discretisationbounded linear operatorsKrylov subspacescyclic operatorsKrylov solutionGMRESconjugate gradientLSQR.Preprint